TSTP Solution File: SWC023+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC023+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 22:01:09 EDT 2022
% Result : Theorem 3.33s 3.57s
% Output : Refutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of clauses : 68 ( 38 unt; 14 nHn; 68 RR)
% Number of literals : 129 ( 0 equ; 55 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(skc5),
file('SWC023+1.p',unknown),
[] ).
cnf(2,axiom,
ssList(skc4),
file('SWC023+1.p',unknown),
[] ).
cnf(6,axiom,
cyclefreeP(nil),
file('SWC023+1.p',unknown),
[] ).
cnf(7,axiom,
totalorderP(nil),
file('SWC023+1.p',unknown),
[] ).
cnf(8,axiom,
strictorderP(nil),
file('SWC023+1.p',unknown),
[] ).
cnf(9,axiom,
totalorderedP(nil),
file('SWC023+1.p',unknown),
[] ).
cnf(10,axiom,
strictorderedP(nil),
file('SWC023+1.p',unknown),
[] ).
cnf(11,axiom,
duplicatefreeP(nil),
file('SWC023+1.p',unknown),
[] ).
cnf(12,axiom,
equalelemsP(nil),
file('SWC023+1.p',unknown),
[] ).
cnf(13,axiom,
neq(skc5,nil),
file('SWC023+1.p',unknown),
[] ).
cnf(52,axiom,
ssList(skf44(u,v)),
file('SWC023+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ ssList(u)
| frontsegP(u,u) ),
file('SWC023+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ ssList(u)
| frontsegP(u,nil) ),
file('SWC023+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ skP0(skc4,skc5)
| equal(nil,skc5) ),
file('SWC023+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ skP0(skc4,skc5)
| equal(nil,skc4) ),
file('SWC023+1.p',unknown),
[] ).
cnf(79,axiom,
( skP0(u,v)
| neq(skf44(u,v),nil) ),
file('SWC023+1.p',unknown),
[] ).
cnf(80,axiom,
( skP0(u,v)
| frontsegP(v,skf44(u,v)) ),
file('SWC023+1.p',unknown),
[] ).
cnf(81,axiom,
( skP0(u,v)
| frontsegP(u,skf44(u,v)) ),
file('SWC023+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ ssList(u)
| ~ frontsegP(nil,u)
| equal(nil,u) ),
file('SWC023+1.p',unknown),
[] ).
cnf(128,axiom,
( ~ ssList(u)
| ~ neq(u,nil)
| ~ frontsegP(skc4,u)
| ~ frontsegP(skc5,u) ),
file('SWC023+1.p',unknown),
[] ).
cnf(188,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(tl(u),tl(v))
| ~ equal(hd(u),hd(v))
| equal(u,v)
| equal(nil,v)
| equal(nil,u) ),
file('SWC023+1.p',unknown),
[] ).
cnf(197,plain,
( ~ skP0(skc4,skc5)
| equal(skc5,skc4) ),
inference(rew,[status(thm),theory(equality)],[69,68]),
[iquote('0:Rew:69.1,68.1')] ).
cnf(246,plain,
( ~ neq(skc4,nil)
| ~ frontsegP(skc5,skc4)
| ~ frontsegP(skc4,skc4) ),
inference(res,[status(thm),theory(equality)],[2,128]),
[iquote('0:Res:2.0,128.0')] ).
cnf(281,plain,
frontsegP(skc4,skc4),
inference(res,[status(thm),theory(equality)],[2,61]),
[iquote('0:Res:2.0,61.0')] ).
cnf(282,plain,
frontsegP(skc4,nil),
inference(res,[status(thm),theory(equality)],[2,62]),
[iquote('0:Res:2.0,62.0')] ).
cnf(287,plain,
( ~ ssList(u)
| ~ equal(tl(skc4),tl(u))
| ~ equal(hd(skc4),hd(u))
| equal(nil,u)
| equal(skc4,u)
| equal(nil,skc4) ),
inference(res,[status(thm),theory(equality)],[2,188]),
[iquote('0:Res:2.0,188.1')] ).
cnf(418,plain,
( ~ neq(skc5,nil)
| ~ frontsegP(skc5,skc5)
| ~ frontsegP(skc4,skc5) ),
inference(res,[status(thm),theory(equality)],[1,128]),
[iquote('0:Res:1.0,128.0')] ).
cnf(453,plain,
frontsegP(skc5,skc5),
inference(res,[status(thm),theory(equality)],[1,61]),
[iquote('0:Res:1.0,61.0')] ).
cnf(454,plain,
frontsegP(skc5,nil),
inference(res,[status(thm),theory(equality)],[1,62]),
[iquote('0:Res:1.0,62.0')] ).
cnf(459,plain,
( ~ ssList(u)
| ~ equal(tl(skc5),tl(u))
| ~ equal(hd(skc5),hd(u))
| equal(nil,u)
| equal(skc5,u)
| equal(nil,skc5) ),
inference(res,[status(thm),theory(equality)],[1,188]),
[iquote('0:Res:1.0,188.1')] ).
cnf(547,plain,
( ~ frontsegP(skc5,skc4)
| ~ neq(skc4,nil) ),
inference(mrr,[status(thm)],[246,281]),
[iquote('0:MRR:246.2,281.0')] ).
cnf(550,plain,
~ frontsegP(skc4,skc5),
inference(mrr,[status(thm)],[418,13,453]),
[iquote('0:MRR:418.0,418.1,13.0,453.0')] ).
cnf(561,plain,
equal(nil,skc5),
inference(spt,[spt(split,[position(s1)])],[459]),
[iquote('1:Spt:459.5')] ).
cnf(647,plain,
frontsegP(skc4,skc5),
inference(rew,[status(thm),theory(equality)],[561,282]),
[iquote('1:Rew:561.0,282.0')] ).
cnf(678,plain,
$false,
inference(mrr,[status(thm)],[647,550]),
[iquote('1:MRR:647.0,550.0')] ).
cnf(766,plain,
~ equal(nil,skc5),
inference(spt,[spt(split,[position(sa)])],[678,561]),
[iquote('1:Spt:678.0,459.5,561.0')] ).
cnf(767,plain,
( ~ ssList(u)
| ~ equal(tl(skc5),tl(u))
| ~ equal(hd(skc5),hd(u))
| equal(nil,u)
| equal(skc5,u) ),
inference(spt,[spt(split,[position(s2)])],[459]),
[iquote('1:Spt:678.0,459.0,459.1,459.2,459.3,459.4')] ).
cnf(782,plain,
equal(nil,skc4),
inference(spt,[spt(split,[position(s2s1)])],[287]),
[iquote('2:Spt:287.5')] ).
cnf(785,plain,
cyclefreeP(skc4),
inference(rew,[status(thm),theory(equality)],[782,6]),
[iquote('2:Rew:782.0,6.0')] ).
cnf(786,plain,
totalorderP(skc4),
inference(rew,[status(thm),theory(equality)],[782,7]),
[iquote('2:Rew:782.0,7.0')] ).
cnf(787,plain,
strictorderP(skc4),
inference(rew,[status(thm),theory(equality)],[782,8]),
[iquote('2:Rew:782.0,8.0')] ).
cnf(788,plain,
totalorderedP(skc4),
inference(rew,[status(thm),theory(equality)],[782,9]),
[iquote('2:Rew:782.0,9.0')] ).
cnf(789,plain,
strictorderedP(skc4),
inference(rew,[status(thm),theory(equality)],[782,10]),
[iquote('2:Rew:782.0,10.0')] ).
cnf(790,plain,
duplicatefreeP(skc4),
inference(rew,[status(thm),theory(equality)],[782,11]),
[iquote('2:Rew:782.0,11.0')] ).
cnf(791,plain,
equalelemsP(skc4),
inference(rew,[status(thm),theory(equality)],[782,12]),
[iquote('2:Rew:782.0,12.0')] ).
cnf(797,plain,
frontsegP(skc5,skc4),
inference(rew,[status(thm),theory(equality)],[782,454]),
[iquote('2:Rew:782.0,454.0')] ).
cnf(800,plain,
~ equal(skc5,skc4),
inference(rew,[status(thm),theory(equality)],[782,766]),
[iquote('2:Rew:782.0,766.0')] ).
cnf(831,plain,
( skP0(u,v)
| neq(skf44(u,v),skc4) ),
inference(rew,[status(thm),theory(equality)],[782,79]),
[iquote('2:Rew:782.0,79.1')] ).
cnf(834,plain,
( ~ frontsegP(skc5,skc4)
| ~ neq(skc4,skc4) ),
inference(rew,[status(thm),theory(equality)],[782,547]),
[iquote('2:Rew:782.0,547.1')] ).
cnf(854,plain,
( ~ ssList(u)
| ~ frontsegP(nil,u)
| equal(skc4,u) ),
inference(rew,[status(thm),theory(equality)],[782,93]),
[iquote('2:Rew:782.0,93.2')] ).
cnf(882,plain,
~ skP0(skc4,skc5),
inference(mrr,[status(thm)],[197,800]),
[iquote('2:MRR:197.1,800.0')] ).
cnf(930,plain,
~ neq(skc4,skc4),
inference(mrr,[status(thm)],[834,797]),
[iquote('2:MRR:834.0,797.0')] ).
cnf(931,plain,
( ~ ssList(u)
| ~ frontsegP(skc4,u)
| equal(skc4,u) ),
inference(rew,[status(thm),theory(equality)],[782,854]),
[iquote('2:Rew:782.0,854.1')] ).
cnf(1012,plain,
( ~ ssList(skf44(skc4,u))
| skP0(skc4,u)
| equal(skf44(skc4,u),skc4) ),
inference(res,[status(thm),theory(equality)],[81,931]),
[iquote('2:Res:81.1,931.1')] ).
cnf(1014,plain,
( skP0(skc4,u)
| equal(skf44(skc4,u),skc4) ),
inference(ssi,[status(thm)],[1012,52,2,785,786,787,788,789,790,791]),
[iquote('2:SSi:1012.0,52.0,2.0,785.0,786.0,787.0,788.0,789.0,790.0,791.0')] ).
cnf(1017,plain,
( skP0(skc4,u)
| skP0(skc4,u)
| neq(skc4,skc4) ),
inference(spr,[status(thm),theory(equality)],[1014,831]),
[iquote('2:SpR:1014.1,831.1')] ).
cnf(1021,plain,
( skP0(skc4,u)
| neq(skc4,skc4) ),
inference(obv,[status(thm),theory(equality)],[1017]),
[iquote('2:Obv:1017.0')] ).
cnf(1022,plain,
skP0(skc4,u),
inference(mrr,[status(thm)],[1021,930]),
[iquote('2:MRR:1021.1,930.0')] ).
cnf(1023,plain,
$false,
inference(unc,[status(thm)],[1022,882]),
[iquote('2:UnC:1022.0,882.0')] ).
cnf(1026,plain,
~ equal(nil,skc4),
inference(spt,[spt(split,[position(s2sa)])],[1023,782]),
[iquote('2:Spt:1023.0,287.5,782.0')] ).
cnf(1027,plain,
( ~ ssList(u)
| ~ equal(tl(skc4),tl(u))
| ~ equal(hd(skc4),hd(u))
| equal(nil,u)
| equal(skc4,u) ),
inference(spt,[spt(split,[position(s2s2)])],[287]),
[iquote('2:Spt:1023.0,287.0,287.1,287.2,287.3,287.4')] ).
cnf(1033,plain,
~ skP0(skc4,skc5),
inference(mrr,[status(thm)],[69,1026]),
[iquote('2:MRR:69.1,1026.0')] ).
cnf(2027,plain,
( ~ ssList(skf44(u,skc5))
| ~ neq(skf44(u,skc5),nil)
| ~ frontsegP(skc4,skf44(u,skc5))
| skP0(u,skc5) ),
inference(res,[status(thm),theory(equality)],[80,128]),
[iquote('0:Res:80.1,128.3')] ).
cnf(6204,plain,
( ~ neq(skf44(u,skc5),nil)
| ~ frontsegP(skc4,skf44(u,skc5))
| skP0(u,skc5) ),
inference(ssi,[status(thm)],[2027,52,1]),
[iquote('0:SSi:2027.0,52.0,1.0')] ).
cnf(6205,plain,
( ~ frontsegP(skc4,skf44(u,skc5))
| skP0(u,skc5) ),
inference(mrr,[status(thm)],[6204,79]),
[iquote('0:MRR:6204.0,79.1')] ).
cnf(7356,plain,
( skP0(skc4,skc5)
| skP0(skc4,skc5) ),
inference(res,[status(thm),theory(equality)],[81,6205]),
[iquote('0:Res:81.1,6205.0')] ).
cnf(7357,plain,
skP0(skc4,skc5),
inference(obv,[status(thm),theory(equality)],[7356]),
[iquote('0:Obv:7356.0')] ).
cnf(7358,plain,
$false,
inference(mrr,[status(thm)],[7357,1033]),
[iquote('2:MRR:7357.0,1033.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC023+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 06:46:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.33/3.57
% 3.33/3.57 SPASS V 3.9
% 3.33/3.57 SPASS beiseite: Proof found.
% 3.33/3.57 % SZS status Theorem
% 3.33/3.57 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.33/3.57 SPASS derived 4713 clauses, backtracked 1252 clauses, performed 72 splits and kept 3366 clauses.
% 3.33/3.57 SPASS allocated 104398 KBytes.
% 3.33/3.57 SPASS spent 0:00:03.11 on the problem.
% 3.33/3.57 0:00:00.04 for the input.
% 3.33/3.57 0:00:00.07 for the FLOTTER CNF translation.
% 3.33/3.57 0:00:00.05 for inferences.
% 3.33/3.57 0:00:00.04 for the backtracking.
% 3.33/3.57 0:00:02.73 for the reduction.
% 3.33/3.57
% 3.33/3.57
% 3.33/3.57 Here is a proof with depth 2, length 68 :
% 3.33/3.57 % SZS output start Refutation
% See solution above
% 3.33/3.57 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax42 ax45 ax46 ax77
% 3.33/3.57
%------------------------------------------------------------------------------